Heading into the international break, Spurs are riding a four-match winning streak that includes an incredible—dare I say, unbelievable?—win at Manchester United. It's the first time the lads of North London have walked into Old Trafford and won a match since 1989.

But there's still an air of incompleteness hanging over Tottenham's roster and supporters can sense that if one or two holes aren't filled with a top-tier, world-class player, they'll be on the outside looking in when it comes to next season's Champions League.

Who should Spurs pursue during January's transfer window? Join me as I present the five signings that fit within Villas-Boas' philosophy and that Tottenham fans would go crazy for.

Radamel Falcao (Atletico Madrid)

Chris Brunskill/Getty Images

Let's start with one that's about as improbable as it gets, but one that would get Spurs fans crazier than a Neil Warnock rant.

Radamel Falcao represents an incredible striker who is starting to come into the prime of his career. He's a plug-and-play kind of guy; shell out the right amount of cash, fit him for a jersey and he can be slotted into any roster and give its offense a shot in the arm.

So what's the problem? Well, he's a world-class striker—everyone and their mother wants him.

Goal.com reported that reigning Premier League champions Manchester City were in attendance to see a recent Atletico Madrid match and that manager Roberto Mancini was personally overseeing them.

Mancini spent next to nothing during this summer's transfer window, so they figure to have enough money saved up to write Atletico Madrid the kind of check that will release Falcao from La Liga.

Tottenham still has some cash from this summer, but it's nowhere near the £48 million ballpark estimate that the Daily Mail is reporting it will take to get Falcao on your roster.

Spurs fans would go crazy, but unless Chairman Daniel Levy dips into next year's transfer budget, this one won't happen.

Loic Remy (Marseille)

Mere hours before this summer's transfer window shut, Goal.com was reporting that after signing Lyon goalkeeper Hugo Lloris, Tottenham was turning their attention toward Marseille striker Loic Remy in a desperate, 11th-hour move to try and add some potency to a lagging Spurs offense.

The deal didn't happen and instead, Clint Dempsey was signed away from Fulham, but Dempsey's more gifted in support, orchestrating things at the top of the key. Remy is the one you want receiving that final touch before it's buried in the back of the net.

The 25-year-old striker has scored no fewer than 11 times every season going back to 2008. He's earned an average of 0.41 goals per match during his career—an incredible feat that would put him at the top of Tottenham's current squad—and he's had significant Champions League experience, appearing in 16 matches over the last two seasons.

His six-foot frame would be a great asset in the air, and yes, I know they just signed one of the most athletic centre-forwards in Emmanuel Adebayor, but Remy's ability to cut inside makes him a danger on the counter-attack, and that's agility they just don't have in Adebayor.

Yes, Jermain Defoe has showed an incredible amount of quality, but right now Tottenham's hopes on offense rest squarely on his shoulders. What if Defoe goes down with a four-month knee injury? What if he starts getting tired trying to balance his club play with England's World Cup qualifiers?

Rasmus Elm (CSKA Moscow)

Oleg Nikishin/Getty Images

There's no question that Tottenham needs help in the center of the pitch. They're not winning the possession game, relying more on quick counter-attacks rather than methodical drives that chew up minutes on the clock.

Enter Rasmus Elm.

The Swedish international who currently features for CSKA Moscow is just as gifted at making interceptions as he is at playing keep-away. He's a big reason why the club finished third in the Russian Premier League last season and why they're just two points out of the lead this season.

He's starting to feature more and more for a Swedish national team that is getting stronger and stronger. Sign the 24-year-old now and you've got the youngster on his rise.

Ömer Toprak (Bayer Leverkusen)

OK, I admit it—Ömer Toprak isn't exactly the kind of player that Tottenham fans would go "crazy" for. Not at the initial signing anyway.

But after one or two matches, they'd start to cheer the Turkish international who currently stars for Bayer Leverkusen.

You may not know it, but Leverkusen conceded only 44 goals through 34 matches—fourth in Bundesliga play last season—and the athletic Toprak was a big reason why.

He's a durable player who made 27 of 34 possible league appearances and also gained some Champions League experience, playing in six of the club's European matches this season. He's physical, he's scrappy and he'd be a superb addition to Tottenham's pool of centre-backs.

Phil Jagielka (Everton)

While Toprak might come a little cheaper, it's Everton's Phil Jagielka who would illicit a few more cheers in North London pubs.

Everton is playing lights out to start this season, ranking fourth in the league table and conceding just eight goals in the first seven matches.

But that's no surprise for any Toffees fan; Everton's had one of the best defenses for years now.

Everton averaged 1.05 goals conceded per match last year, third only to Manchester City's 0.76 and Manchester United's 0.87. American goalkeeper Tim Howard did his job last season, but so did Everton centre-backs Phil Jagielka and John Heitinga.

Jagielka is fearless in the air and willing to put his body on the line if it means getting a ball out of danger.